SCALE FACTOR
Find a scale factor, enlarge a length or work backwards to the original size
Useful for GCSE maths enlargement and reduction questions
MODE
FIND
Choose FIND or APPLY
ROUNDING
2DP
Round the final result
ORIGINAL
A
Starting length
NEW
B
Length after scaling
WORKING
—
—
—
—
—
RESULT
READY
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PAGE SUMMARY
Use this page to find a scale factor from two matching lengths or apply a known scale factor.
It handles enlargement and reduction questions clearly with step-by-step working.
Good for GCSE maths scale factor, enlargement ratio and reduction problems.
More formula help, examples and internal links are on the next pages.
Page 1 stays focused on the calculator so the inputs remain visible on laptops, tablets and phones.
Use the example button for a quick enlargement example with scale factor 2.4.
HOW TO USE
1) Choose MODE.
2) Enter the lengths or scale factor.
3) Press SOLVE.
4) Read the working and result.
FIND SCALE FACTOR
k = NEW ÷ ORIGINAL
If k is bigger than 1, the shape is enlarged.
If k is between 0 and 1, the shape is reduced.
APPLY SCALE FACTOR
NEW = ORIGINAL × k
ORIGINAL = NEW ÷ k
Keep the units the same throughout.
CHECKS
Original length cannot be zero when finding k.
Scale factor cannot be zero when working back to the original length.
PAGE 2/4
WORKED EXAMPLE 1
Original length = 5
New length = 12
k = 12 ÷ 5
k = 2.4
This is an enlargement.
WORKED EXAMPLE 2
Original length = 18
Scale factor = 0.5
NEW = 18 × 0.5
NEW = 9
This is a reduction.
WORKED EXAMPLE 3
New length = 15
Scale factor = 3
ORIGINAL = 15 ÷ 3
ORIGINAL = 5
GCSE TIP
Scale factor compares matching lengths, not areas or volumes.
Make sure you compare like with like.
PAGE 3/4
SEO / HELP PAGE
This page supports searches for scale factor calculator, enlargement calculator, reduction calculator and find scale factor from lengths.
It is useful for GCSE maths revision on enlargement and reduction.
RELATED PAGES
USEFUL WORDING
Enlargement means multiply by a scale factor greater than 1.
Reduction means multiply by a scale factor between 0 and 1.
LOOP BACK
Use NEXT to return to Page 1 and carry on calculating.
PAGE 4/4
MODE
FIND
Choose FIND or APPLY
ROUNDING
2DP
Round the final result
ORIGINAL
A
Starting length
NEW
B
Length after scaling
WORKING
—
—
—
—
—
RESULT
READY
—
PAGE 1/4
HOW TO USE
1) Choose MODE.
2) Enter the lengths or scale factor.
3) Press SOLVE.
4) Read the working and result.
FIND SCALE FACTOR
k = NEW ÷ ORIGINAL
k bigger than 1 means enlargement.
k between 0 and 1 means reduction.
APPLY SCALE FACTOR
NEW = ORIGINAL × k
ORIGINAL = NEW ÷ k
Use the same units throughout.
CHECKS
Original length cannot be zero when finding k.
Scale factor cannot be zero when finding the original length.
PAGE 2/4
WORKED EXAMPLE 1
Original length = 5
New length = 12
k = 12 ÷ 5
k = 2.4
This is an enlargement.
WORKED EXAMPLE 2
Original length = 18
Scale factor = 0.5
NEW = 18 × 0.5
NEW = 9
This is a reduction.
WORKED EXAMPLE 3
New length = 15
Scale factor = 3
ORIGINAL = 15 ÷ 3
ORIGINAL = 5
GCSE TIP
Scale factor compares matching lengths, not areas or volumes.
PAGE 3/4
GCSE SCALE FACTOR HELP
This page supports searches for scale factor calculator, enlargement calculator, reduction calculator and find scale factor from lengths.
RELATED PAGES
USEFUL WORDING
Enlargement means multiply by a scale factor greater than 1.
Reduction means multiply by a scale factor between 0 and 1.
LOOP BACK
Use NEXT to return to Page 1 and solve another question.
PAGE 4/4